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Huygens metasurface (HMS) provides a flexible way to tailor the phases of fields without incurring reflection. Recently, HMS has been used in antenna scenes to convert the incident field into directional radiation. However, most design processes of the HMS antennas are based on the generalized sheet transition condition, which is usually augmented with extra operations for ensuring passivity and losslessness. Here, we propose a simple and comprehensive strategy to design and optimize the HMS antenna. The strategy builds an equivalent model of the HMS antenna and deals with the designs from the perspective of phase optimization, which is simple and straightforward. A fast and efficient algorithm is presented to solve the optimization problem under the framework of alternating direction method of multipliers (ADMM). The phases obtained by this strategy are naturally compatible with the passive and lossless conditions and can be directly implemented by metasurfaces. Furthermore, the strategy imposes constraints on the phase difference of adjacent meta-atoms, thus reducing the performance deterioration caused by aperiodic boundary conditions. The feasibility and superiority of the strategy are verified by full-wave simulation results and experimental measurements of exemplary designs.